Determine the average rate of change of 𝑦 in the function 𝑦=2𝑥3+7𝑥2+2𝑥−3 over the interval [3, 5].

To determine the average rate of change of the function y = 2x³ + 7x² + 2x - 3 over the interval [3, 5], you need to follow these steps:

1. Substitute the x-values of the interval into the function to find the corresponding y-values.

   For x = 3, y = 2(3)³ + 7(3)² + 2(3) - 3 = 108.

   For x = 5, y = 2(5)³ + 7(5)² + 2(5) - 3 = 312.

2. Use the formula for the average rate of change, which is (f(b) - f(a)) / (b - a), where [a, b] is the interval.

   So, the average rate of change is (312 - 108) / (5 - 3) = 204 / 2 = 102.

Therefore, the average rate of change of the function y = 2x³ + 7x² + 2x - 3 over the interval [3, 5] is 102.